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A010972
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a(n) = binomial(n,19).
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8
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1, 20, 210, 1540, 8855, 42504, 177100, 657800, 2220075, 6906900, 20030010, 54627300, 141120525, 347373600, 818809200, 1855967520, 4059928950, 8597496600, 17672631900, 35345263800, 68923264410, 131282408400, 244662670200, 446775310800, 800472431850
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OFFSET
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19,2
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COMMENTS
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).
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FORMULA
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a(n+18) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)*(n+8)*(n+9)*(n+10)*(n+11)*(n+12)*(n+13)*(n+14)*(n+15)*(n+16)*(n+17)*(n+18)/19!. - Artur Jasinski, Dec 02 2007; R. J. Mathar, Jul 07 2009
Sum_{n>=19} 1/a(n) = 19/18.
Sum_{n>=19} (-1)^(n+1)/a(n) = A001787(19)*log(2) - A242091(19)/18! = 4980736*log(2) - 10574853703013/3063060 = 0.9542064261... (End)
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MAPLE
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MATHEMATICA
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PROG
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(PARI) vector(25, n, binomial(n+18, 19)) \\ G. C. Greubel, Nov 23 2017
(SageMath) [binomial(n, 19) for n in (19..45)] # G. C. Greubel, Aug 27 2019
(GAP) List([19..45], n-> Binomial(n, 19) ); # G. C. Greubel, Aug 27 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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